Acronym | pabidrid, J80 |
Name | parabidiminished rhombicosidodecahedron |
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Circumradius | sqrt[sqrt(5)+11/4] = 2.232951 |
Vertex figures | [4,5,10], [3,4,5,4] |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
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Face vector | 50, 90, 42 |
Confer |
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External links |
This polyhedron is an edge-faceting of the small rhombicosidodecahedron (srid).
Incidence matrix according to Dynkin symbol
xxFofx5xfoFxx&#xt → height(1,2) = height(5,6) = sqrt[(5+sqrt(5))/10] = 0.850651 height(2,3) = height(4,5) = sqrt[(5-sqrt(5))/10] = 0.525731 height(3,4) = sqrt[(5-2 sqrt(5))/5] = 0.324920 o.....5o..... | 10 * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 at top {10} .o....5.o.... | * 10 * * * * | 0 0 1 1 1 1 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 ..o...5..o... | * * 5 * * * | 0 0 0 0 2 0 2 0 0 0 0 0 | 0 0 1 0 2 1 0 0 0 ...o..5...o.. | * * * 5 * * | 0 0 0 0 0 2 0 2 0 0 0 0 | 0 0 0 1 2 0 1 0 0 ....o.5....o. | * * * * 10 * | 0 0 0 0 0 0 1 1 1 1 0 0 | 0 0 0 0 1 1 1 1 0 .....o5.....o | * * * * * 10 | 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 0 1 1 1 at bottom {10} ------------------+-----------------+-------------------------------+------------------- x..... ...... | 2 0 0 0 0 0 | 5 * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 {4},{10}-join ...... x..... | 2 0 0 0 0 0 | * 5 * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 {5},{10}-join oo....5oo....&#x | 1 1 0 0 0 0 | * * 10 * * * * * * * * * | 0 1 1 0 0 0 0 0 0 .x.... ...... | 0 2 0 0 0 0 | * * * 5 * * * * * * * * | 0 1 0 1 0 0 0 0 0 .oo...5.oo...&#x | 0 1 1 0 0 0 | * * * * 10 * * * * * * * | 0 0 1 0 1 0 0 0 0 .o.o..5.o.o..&#x | 0 1 0 1 0 0 | * * * * * 10 * * * * * * | 0 0 0 1 1 0 0 0 0 ..o.o.5..o.o.&#x | 0 0 1 0 1 0 | * * * * * * 10 * * * * * | 0 0 0 0 1 1 0 0 0 ...oo.5...oo.&#x | 0 0 0 1 1 0 | * * * * * * * 10 * * * * | 0 0 0 0 1 0 1 0 0 ...... ....x. | 0 0 0 0 2 0 | * * * * * * * * 5 * * * | 0 0 0 0 0 1 0 1 0 ....oo5....oo&#x | 0 0 0 0 1 1 | * * * * * * * * * 10 * * | 0 0 0 0 0 0 1 1 0 .....x ...... | 0 0 0 0 0 2 | * * * * * * * * * * 5 * | 0 0 0 0 0 0 1 0 1 {5},{10}-join ...... .....x | 0 0 0 0 0 2 | * * * * * * * * * * * 5 | 0 0 0 0 0 0 0 1 1 {4},{10}-join ------------------+-----------------+-------------------------------+------------------- x.....5x..... | 10 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * top {10} xx.... ......&#x | 2 2 0 0 0 0 | 1 0 2 1 0 0 0 0 0 0 0 0 | * 5 * * * * * * * ...... xfo...&#xt | 2 2 1 0 0 0 | 0 1 2 0 2 0 0 0 0 0 0 0 | * * 5 * * * * * * .x.o.. ......&#x | 0 2 0 1 0 0 | 0 0 0 1 0 2 0 0 0 0 0 0 | * * * 5 * * * * * .oooo.5.oooo.&#xr | 0 1 1 1 1 0 | 0 0 0 0 1 1 1 1 0 0 0 0 | * * * * 10 * * * * cycle(BCED) ...... ..o.x.&#x | 0 0 1 0 2 0 | 0 0 0 0 0 0 2 0 1 0 0 0 | * * * * * 5 * * * ...ofx ......&#xt | 0 0 0 1 2 2 | 0 0 0 0 0 0 0 2 0 2 1 0 | * * * * * * 5 * * ...... ....xx&#x | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * 5 * .....x5.....x | 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 0 5 5 | * * * * * * * * 1 bottom {10}
or o.....5o..... & | 20 * * | 1 1 1 0 0 0 | 1 1 1 0 0 polar, at {10} .o....5.o.... & | * 20 * | 0 0 1 1 1 1 | 0 1 1 1 1 tropical ..o...5..o... & | * * 10 | 0 0 0 0 2 2 | 0 0 1 1 2 medial --------------------+----------+-------------------+-------------- x..... ...... & | 2 0 0 | 10 * * * * * | 1 1 0 0 0 {4},{10}-join ...... x..... & | 2 0 0 | * 10 * * * * | 1 0 1 0 0 {5},{10}-join oo....5oo....&#x & | 1 1 0 | * * 20 * * * | 0 1 1 0 0 .x.... ...... & | 0 2 0 | * * * 10 * * | 0 1 0 1 0 .oo...5.oo...&#x & | 0 1 1 | * * * * 20 * | 0 0 1 0 1 {4},{5}-join .o.o..5.o.o..&#x & | 0 1 1 | * * * * * 20 | 0 0 0 1 1 {3},{4}-join --------------------+----------+-------------------+-------------- x.....5x..... & | 10 0 0 | 5 5 0 0 0 0 | 2 * * * * {10} xx.... ......&#x & | 2 2 0 | 1 0 2 1 0 0 | * 10 * * * polar {4} ...... xfo...&#xt & | 2 2 1 | 0 1 2 0 2 0 | * * 10 * * {5} .x.o.. ......&#x & | 0 2 1 | 0 0 0 1 0 2 | * * * 10 * {3} .oooo.5.oooo.&#xr | 0 2 2 | 0 0 0 0 2 2 | * * * * 10 equatorial {4}, cycle(BCED)
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